Properties of Logarithms
Objectives: 1. Apply the change of base formula to rewrite logarithms with different bases.
2. Use properties of logarithms to evaluate or rewrite logarithmic expressions.
3. Use properties of logarithms to expand or condense logarithmic expressions.
4. Use logarithms to model and solve real­life problems.
Nov 4­7:41 PM
P.O.D. Sketch the graph of y = y
6
5
4
3
2
1
­6
­5
­4
­3
­2
­1
0
­1
x
1
2
3
4
5
6
­2
­3
­4
­5
­6
Nov 4­7:46 PM
P.O.D. Solve each logarithm
1. 3. 2. 4. Nov 8­7:43 AM
1
Change of Base Formula
Examples: 1. 2.
Nov 4­7:49 PM
Properties of Logarithms
Let a be a positive number such that a 1,
and let n be a real number. If u and v are positive numbers, the following properties are true.
1. Product Property
2. Quotient Property
3. Power Property
Nov 4­7:58 PM
Write each logarithm in terms of 2 and 3
1. ln 6=ln(2 3)
2. Nov 4­8:10 PM
2
Use the properties to expand each expression.
1. 2. ln
Nov 4­8:14 PM
Use the properties of logarithms to condense each logarithmic expression.
1. 2. 3. Nov 4­8:19 PM
Closure
Find the exact value of the logarithm without using a calculator.
Nov 4­8:27 PM
3
Assignment 5 and 6
Nov 4­8:32 PM
4